Though I don't know any way of solving the original poster's problem simply
and effectively, I don't think it's fair to say that it is "something that
can't be effectively implemented". Just as today we can declare that
equal(e,1), we could in principle support assume(equal(abs(e),1)). Alas,
Maxima can't do much of interest with that fact, not even "easy" things
like is(equal(e,0)) => false and is(e<2) => true. Another possible way of
expressing the fact is assume(equal(e,1) or equal(e,-1)), but Maxima
doesn't allow that at all.
-s
On Fri, Apr 13, 2012 at 11:42, Richard Fateman <fateman at eecs.berkeley.edu>wrote:
> In some sense the original poster is asking for something that can't be
> effectively implemented.
> At least as I read it, the question is, can Maxima handle this situation:
>
> "I'm thinking of a number, either one or minus one. Call it e. I'm going
> to
> write an expression (trigonometric, but really e*x is not trig..)
> involving exactly one occurrence of e.
> I want it simplified for either value of e, but with the result expressed
> as a function
> of e, in a nice form."
>
>
> Well, look at this: sin(3.0+e). What are you going to do? How about
> 0^e?
>
> The original question is really such a special special case that it seems
> unlikely to
> be a built-in "feature". On the other hand, a computer algebra system has
> lots
> of features and it is hard, especially for a new user, to gather what has
> been
> implemented or not. There are a fair number of peculiar functionalities
> which
> are included not so much because they are useful, but because they could be
> programmed.
>
> There is a reasonable approach if you are willing to reformulate the
> problem as
> actions on pairs, as suggested.
>
> instead of sin(e*x), use {sin(x), sin(-x)}.
>
> If both elements are identical, convert to a single value. Otherwise, all
> operations are
> mapped on to each of the two values. Doing this systematically might be
> possible by
> some cleverness.
>
> RJF
>
>
>
> On 4/13/12 8:17 AM, Barton Willis wrote:
>
>> The general simplifier for trigonometric functions has a method for
>> deciding when to apply a reflection identity; for example
>>
>> (%i1) sin(-x);
>> (%o1) -sin(x)
>>
>> (%i2) cos(-x);
>> (%o2) cos(x)
>>
>> (%i3) makelist(cos(x + (1-e) * %pi/2),e,[-1,0,1]);
>> (%o3) [-cos(x),-sin(x),cos(x)]
>>
>> Maxima uses an ordering predicate (defined on expressions, not just
>> numbers) to decide when to use the reflection identity:
>>
>> (%i4) sin(b-x);
>> (%o4) -sin(x-b)
>>
>> (%i5) sin(b-a);
>> (%o5) sin(b-a)
>>
>> The aim of the algorithm is to simplify as many expressions to zero as
>> possible:
>>
>> (%i7) sin(b-x) + sin(x-b);
>> (%o7) 0
>>
>> (%i8) sin(a-b) + sin(b-a);
>> (%o8) 0
>>
>> Also, the function trigrat might be useful to you? I didn't answer your
>> question, but maybe some of this is useful.
>>
>> --bw
>>
>> ______________________________**__________
>> From: maxima-bounces at math.utexas.edu [maxima-bounces at math.utexas.**edu<maxima-bounces at math.utexas.edu>]
>> on behalf of Jean Vittor [jean.vittor at free.fr]
>> Sent: Friday, April 13, 2012 06:39
>> To: maxima at math.utexas.edu
>> Subject: simplification
>>
>> Hi,
>>
>> I'm new to maxima and I have a hard time understanding how
>> simplification works.
>>
>> My point is to use "sign" values (I mean integers which take their value
>> from {-1;1}) and to be able to automate some trigo simplifications like
>> (in the following, e is a sign and x a real expression):
>> - sin(e*x) -> e*sin(x)
>> - cos(e*x) -> cos(x)
>> - cos(x+(1-e)*%pi/2) -> e*cos(x)
>> - ...
>> - and, of course, e^2 -> 1
>>
>> Is there a way to do this with maxima ?
>>
>>
>> Thanks,
>>
>> Jean
>>
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